With the rapid advancement of large language models (LLMs) and robotics, service robots are increasingly becoming an integral part of daily life, offering a wide range of services in complex environments. To deliver these services intelligently and efficiently, robust and accurate task planning capabilities are essential. This paper presents a comprehensive overview of the integration of LLMs into service robotics, with a particular focus on their role in enhancing robotic task planning. First, the development and foundational techniques of LLMs, including pre-training, fine-tuning, retrieval-augmented generation (RAG), and prompt engineering, are reviewed. We then explore the application of LLMs as the cognitive core-`brain'-of service robots, discussing how LLMs contribute to improved autonomy and decision-making. Furthermore, recent advancements in LLM-driven task planning across various input modalities are analyzed, including text, visual, audio, and multimodal inputs. Finally, we summarize key challenges and limitations in current research and propose future directions to advance the task planning capabilities of service robots in complex, unstructured domestic environments. This review aims to serve as a valuable reference for researchers and practitioners in the fields of artificial intelligence and robotics.